Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 [less than or equal] r [less than or equal] 1 for expansions and r [greater than or equal] 1 for compressions. The particular cases of free expansion and reversible adiabatic processes correspond to r = 0 and r = 1, respectively. To conclude the interpretation of r, the relation between r and the variation of the system entropy was also obtained. Comparison between this study and one restricted to expansions following a microscopic point of view showed not only equivalent interpretations but also that our approach is more general, since it also comprises compressions, provides an objective relation between r and entropy change and considers instantaneous varying values of the adiabatic reversibility coefficient. Finally, simulations of selected adiabatic processes are performed and numerical calculations of r are presented. This paper is intended primarily for the undergraduate student, although a comparison with the aforementioned work also requires a background in thermodynamics and kinetic theory. (Contains 1 figure and 1 table.)